<html lang="en">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>normalize</title>
<style type="text/css">
	body {background-color: white; color: black; font-family:sans-serif; font-size:medium;}
	a:link {color: #3300ff;}
	a:visited {color: #663399;}
	a:hover {color:#0099ff;}
	a:active {color: #0066cc;}
	a.button {text-decoration:none;}
	
	table.nav  {background-color: #dbddff;}
	table.body {margin-top:2ex; margin-bottom:2ex;}
	table.programlistingindent {margin-left:32px;}
	
	img { margin-bottom:0px; margin-top:0px;}
	tt {margin-left:0.5em; margin-right:0.5em; font-weight:lighter;}
	
	p {margin-top:0ex;}
	p.synopsis {margin-left:32px;}
	p.programlistingindent {margin-left:32px;}
	p.citetitle {margin-left:2em;}
	
	ul ul {list-style-type:square;}
	ul li p {margin-top:0ex; margin-bottom:.5ex; padding:0}
	ol li p {margin-top:0ex; margin-bottom:.5ex; padding:0}
	
	h1.reftitle {color:#a90000;}
	h1.reftitle {font-size:3.7ex; margin-top:0; margin-bottom:0; font-weight:bold}
	h1.title {color:black; font-size:4ex; margin-top:1ex; font-weight:bold}
	h2.title {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:3ex}
	h3.title {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2.5ex}
	h4.title {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2ex}
	h2 {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2.5ex}
	h3 {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2ex} 
	
	pre.programlisting {margin-left:32px;}
	pre.synopsis {margin-left:32px;}
	
	
	.categorytitle {margin-top:8px; padding-top:0px;}
	.categorylist {background-color: #e1e6f2;}
 	</style>
</head>
<body>
<a name="top_of_page"></a><p style="font-size:1px;"></p>
<h1 class="reftitle">normalize</h1>
<h2>Purpose</h2>
<p>Normalizes polyhedron in H-representation.</p>
<h2>Syntax</h2>
<pre class="synopsis">P.normalize</pre>
<pre class="synopsis">normalize(P)</pre>
<h2>Description</h2>
<p></p>
        Normalize polyhedron by scaling each inequality <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/normalize1.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/normalize1.png"> 
        and equality <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/normalize2.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/normalize2.png"> such that each row has unitary
        norm, i.e. <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/normalize3.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/normalize3.png"> and <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/normalize4.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/normalize4.png">.
        The normalization routine is very useful to prevent from numerical problems
        involved in badly scaled polyhedra.
	<h2>Input Arguments</h2>
<table cellspacing="0" class="body" cellpadding="4" border="0" width="100%">
<colgroup>
<col width="31%">
<col width="69%">
</colgroup>
<tbody><tr valign="top">
<td><tt>P</tt></td>
<td>
<p></p>
         <tt>Polyhedron</tt> object.<p>
	    		Class: <tt>Polyhedron</tt></p>
</td>
</tr></tbody>
</table>
<h2>Example(s)</h2>
<h3>Example 
				1</h3> Badly scaled polyhedron <pre class="programlisting"> P = Polyhedron([1000, 0.4, -351; -0.1, -1e4, 89.1],[780; 0.067]); </pre>
<pre class="programlisting"></pre> The values are stored inside the polyhedron as they are provided. <pre class="programlisting"> P.H </pre>
<pre class="programlisting">
ans =

                      1000                       0.4                      -351                       780
                      -0.1                    -10000                      89.1                     0.067

</pre> Normalize the polyhedron. <pre class="programlisting"> P.normalize </pre>
<pre class="programlisting">Polyhedron in R^3 with representations:
    H-rep (redundant)   : Inequalities   2 | Equalities   0
    V-rep               : Unknown (call computeVRep() to compute)
Functions : none
</pre> The values of H-representation have changed: <pre class="programlisting"> P.H </pre>
<pre class="programlisting">
ans =

         0.943563707881528      0.000377425483152611        -0.331190861466416         0.735979692147592
     -9.99960308263276e-06        -0.999960308263276       0.00890964634662579      6.69973406536395e-06

</pre>
<h2>See Also</h2>
<a href="./polyhedron.html">polyhedron</a><p></p>
<table class="nav" summary="Navigation aid" border="0" width="100%" cellpadding="0" cellspacing="0"><tr valign="top">
<td align="left" width="20">
<a href="b.html" class="button">&#9664;</a>  </td>
<td align="left">b</td>
<td>  </td>
<td align="right">uminus</td>
<td align="right" width="20"><a href="uminus.html" class="button">&#9654;</a></td>
</tr></table>
<br><p>©  <b>2010-2013</b>     Martin Herceg: ETH Zurich,    <a href="mailto:herceg@control.ee.ethz.ch">herceg@control.ee.ethz.ch</a></p>
</body>
</html>
